Chemistry

Chemistry

Problem

If a0a_0 be the radius of first Bohr orbit of H-atom, the de Broglie wavelength of an electron moving in the III Bohr orbit is : a. 6πa06\pi a_0 b. 2πa02\pi a_0 c. 4πa04\pi a_0 d. πa0\pi a_0
Intuitive explanation

The key is recognizing that the de Broglie wavelength depends on the electron's momentum, which changes as you move to higher Bohr orbits. In the third orbit, the electron moves slower than in the first orbit, so its wavelength will be longer. Use the relationship between orbital radius, velocity, and momentum in Bohr's model—specifically that mvr=nℏmvr = n\hbar—to find the momentum in the third orbit, then apply λ=h/p\lambda = h/p.

Intuitive explanation

The key is recognizing that the de Broglie wavelength depends on the electron's momentum, which changes as you move to higher Bohr orbits. In the third orbit, the electron moves slower than in the first orbit, so its wavelength will be longer. Use the relationship between orbital radius, velocity, and momentum in Bohr's model—specifically that mvr=nℏmvr = n\hbar—to find the momentum in the third orbit, then apply λ=h/p\lambda = h/p.

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